The warping degree of a knot diagram

Details The warping degree of a knot diagram The warping degree of a knot diagram

2008-09-08

arxiv.org/abs/0809.1334v4

Mathematics

Geometric Topology

12 pages, 9 figures

Scientific paper

For an oriented knot diagram D, the warping degree d(D) is the smallest
number of crossing changes which are needed to obtain the monotone diagram from
D in the usual way. We show that d(D) + d(-D) + 1 is less than or equal to the
crossing number of D. Moreover the equality holds if and only if D is an
alternating diagram.

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